ISSN 1450–3417 http://www.biolinguistics.eu Biolinguistics 9: 074-095, 2015
Brain Oscillatory Structures
Javier Ramírez Fernández
From the perspective of brain oscillations, an explanation is offered as to why external systems of language cannot deal with identical categorial elements in certain local domains. An equivalent locality effect in brain structure is argued for which causes a (cognitively problematic and ambiguous) synchronization of rhythms in the gamma, beta1, and beta2 bands. These rhythms can be related to different categories, and their limited patterns and interactions may explain syntactic constraints on phrases, phases, and Internal Merge.
Keywords: brain oscillations; constraints; dynomics; labeling; locality
1 Introduction and Background
One of the most extensively investigated issues in linguistics is locality: Operations take place within concrete domains or chunks of structure, which is manifested in turn by the cyclicity of the derivation. At first glance, two kinds of locality constraints are discernible in language: within domains, or short-distance, and across domains, or long-distance. However, the cyclicity of operations like Internal Merge (IM, traditionally known as movement) makes it possible to reduce constraints across domains, keeping them within. These domains could be phrases or phases; in fact, there are recent studies which argue that phrases and phases are very close to each other (Epstein & Seely 2002, Müller 2004) and strongly correlated to projection or labeling (Narita 2012, Boeckx 2014a).
Inspired by Boeckx (2008) and his unification of the products of External Merge (EM) and IM, where projection is treated equally in phrases and chains, I offer an explanation about combinatorial or interpretative constraints within (and apparently across) locality domains, in a phase-like fashion, from a single logic. Concretely, the constraints will be couched in terms of brain oscillations (Buzsáki 2006), roughly: They arise from the limited oscillatory patterns that
certain local brain structures can sustain. This is a first expansion of the research first and originally presented in Ram´ırez (2014).
Brain oscillations are the emergent mechanism by which brain activity is self-organized (Buzs´aki 2006). Biophysical properties of brain components and their interactions locally and globally submit brain activity to rhythmic patterns, as re-flected by electroencephalographies and magnetoencephalographies (see chapter 4 of Buzs´aki 2006 for an overview about recording methods). At different spatial scales, periods of high activity resulting from the synchrony of neural excitation— within miliseconds time windows—alternate with periods of low activity produced by coordinated inhibition. Such phases enable, respectively, the integration and segregation of information, forming assemblies (Hebb 1949) both at the level of coherent representations (Gray & Singer 1989, Engel & Singer 2001) and transient networks (Fries 2005). There is not a unique brain oscillation but a huge amount at multiple frequencies ranging from .05Hz to 500Hz (Buzs´aki & Draguhn 2004). The most popular bands aredelta(1-4Hz),theta(4-7Hz),alpha(8-14Hz),beta(15-29Hz), andgamma(30-90Hz).
The principles governing these oscillations can be explanatory regarding lo-cality. From a cognitive perspective, the constraints are roughly reflected by a con-flict at the ’external systems’ interpreting *XX-like constructions. We will name this phenomenon ’anti-identity’, based on the work of Richards (2010) and Boeckx (2014a). Intra-phasally, these authors note that phase complements cannot contain two identical categorial elements (2). However, this can also be reflected by selec-tion constraints within phrases (1).1
(1) a. * Johnv[ eat [apples] [oranges] ]. b. * [. . . [John] [Mary]v[eat apples]].
c. * V X X / X X V (2) a. *sono
are [queste these foto pictures del of-the muro] wall [la the causa cause della of-the rivolta]. riot Italian
’These pictures of the wall are the cause of the riot’.
(adapted from Moro 2000) b. *Describieron described [a to un a maestro master de of zen] zen [al to-the papa]. Spanish pope
’They described a Zen master to the pope’.
(adapted from Boeckx 2008) c. * V X X
Similarly, Grohmann (2000, 2011) points to an ”anti-locality” constraint (3), which, very roughly, bans (movement) dependencies in local chunks of structure that are transferred to the external systems (unless repaired later by a sort of spell-out mechanism). Despite their similarity to phases at first glance, Grohmann (2011) restricts these chunks to ’Prolific Domains’ where thematic, agreement and dis-course relationships are established (which would correspond tovP, TP, and CP).
(3) a. *... T ... [Johnilikes ti].2
(adapted from Grohmann 2011) b. * [X V X]
To put it in broad terms, depending on whether the local domain (3) is con-sidered VP orvP (see Larson 1988, Hale & Keyser 1993), at least two kinds of anti-locality can be defended. As discussed by Grohmann (2011), a more classical ap-proach to anti-locality takes the relevant domain to be XP, so intra-phrasally there is a maximum of one occurrence of each element. In contrast, a more recent approach, consistent with Grohmann’s particular perspective, takes the relevant domain to be larger, so there is a maximum of an occurrence of each element within each prolific domain.
A third approach would consist of defending that the relevant domain in (3) is a phase complement, which would bring anti-locality and anti-identity very close to each other. However, a more elegant idea, a truly attractive one, is to unify these three possibilities, arguing that the relevant domain in (3) is at the same time a phrase and a phase, which in turn corresponds to the interpretatively coherent units at the interfaces that Grohmann’s Prolific Domains define.
In this respect, Grohmann (2011) remarks the appeal of fusing ’standard’ lo-cality with ’anti-lolo-cality’ domains, although this would be ”by no means neces-sary”. Nevertheless, to deepen our understanding of these strikingly similar lo-cality phenomena, such unification may be ”by all means necessary”. For space reasons, I will not go into details, but it should be noted that the arguments against such unification are rather weak. It has been argued that intra-phrasal anti-locality is redundantly barred by Last Resort considerations or a ban on vacuous oper-ations; however, given the present assumption that Merge is free and the abuse of feature-driven explanations (Boeckx 2014a), these counterarguments lose their strength. Besides, it has been argued that Prolific Domains differ from phases in that the first are three, whereas the latter only two (vP and CP); in spite of that, phases begin to be related to deeper requisites for syntactic derivations (Boeckx 2014a), providing a category-neutral definition of them rather than recasting old concepts of barrier nodes (Boeckx & Grohmann 2007b).3 Finally, M ¨uller (2004, 2011) argued for an unification of phrases and phases, and for a reformulation of the Phase Impenetrability Condition (Chomsky 2000, 2001), in phrasal terms. This approach is based, among other reasons, on the lack of correspondence be-tween spell-out domains and classical Chomskyan phases, and the successive cyclic movement through every phrase edge (Boeckx 2003), as reflected by morphologi-cal side-effects, reconstruction operations, etc. Even though one may think that M ¨uller’s (2004, 2011) approach suffers from ’featuritis’ (Boeckx 2010) and that con-straints such as Ph(r)ase Balance (Heck & M ¨uller 2000, M ¨uller 2004) may not be so persuasive, I think that defining (anti-)local domains as phrasal provides us at least with a theoretically superior alternative (see Boeckx 2007). In sum, it is not illogi-cal to analyze anti-loillogi-cality in the same terms that anti-identity is approached in the present article.
2 Classical movement traces are adopted only for expository purposes.
Inter-phasally, minimality effects have been noted since Katz’s (1964) A-over-A principle (for a review, see Lahne 2012), where elements higher in the structure, but below the probe (Chomsky 2001), act as interveners for or blockers to the move-ment of lower elemove-ments of the same type (Rizzi 1990). This is illustrated in (4).
(4) a. How do you think [ hev[behaved (how)] ]?
(adapted from Rizzi 2011) b. *How do [ whov[behaved (how)] ]?
c. V [...X... [...X...]]
The aim of this paper is to explain all these locality constraints from a sin-gle principle couched in brain oscillatory terms: The brain tends to synchronize its activity (Buzs´aki 2006), which in turn conditions the patterns that local peripheral language regions can sustain. Regarding the ’periphery of language regions’, we will follow Boeckx’s (2014b) suggestion to reverse the mainstream neurolinguis-tic assumption that language relies on a core set of specific regions, that is tran-siently assisted by a structuralperiphery, responsible for domain general operations (Fedorenko & Thompson-Schill 2014). On the contrary, once language is decom-posed (Poeppel 2012), the best candidate for its mechanisms could be provided by the temporal dynamics of domain general regions (Boeckx & Ben´ıtez-Burraco 2014, Ram´ırezet al.2015). The latter would form the actual languagecore, while the pe-riphery would be limited to subareas of the classical Broca—Wernicke model (see Friederici 2011 for a review), where more specific computations would take place.
To explain all the apparently distinct constraints above from a single princi-ple in classical language subareas, it is needed to equate what seems to be locality across domains to locality within domains. For cases like (4), the cyclic nature of IM allows us to extend the *XX constraint we see in phase complements (2) to IM (3), as Chomsky (2013) points towards. Thus, as (5) shows, both elements involved in the apparent inter-phasal restriction arenotin different domains when the constraint actually applies.
(5) a. *How do you wonder [ who (how)v[behaved (how)] ]?
(adapted from Rizzi 2011) b. *V [...X X... [...]]
theta,alpha, andbetarhythms, respectively, may enable neural syntax (Buzs´aki 2010, Buzs´aki & Watson 2012) of a higher complexity (Ram´ırezet al.2015).
A review of the cognitive neuroscience literature will suggest that non-Phase Heads (PHs) may oscillate atgamma, that transitive PHs—those with complex com-plements Boeckx (2014a)—would do so atbeta2, and that intransitive PHs—those with singleton complements—oscillate atbeta1. In fact, this triangle represents the three elements of phrases/phases: complement, head, and specifier/edge. In like manner, a review of the theoretical linguistics literature will suggest that intransi-tive PH, specifiers and internally merged elements might be unified, in the present model, under the samebeta1categorial rhythm. This will allow us to explain con-straints on ph(r)ase structure and movement across domains in the same terms used intra-ph(r)asally. Finally, some space will be devoted to constraints on ad-junction and alternatives to the proposed implementation.
To explain the constraints that cause these linguistic properties, I will develop the idea that regions of peripheral systems that interpret the three kinds of items listed above can only sustain a maximum of one rhythm for each of their respec-tive bands. This is so because the structure would be too small to sustain them separately if multiple rhythms were to be initially generated. Since synchrony in the same band becomes mandatory and each band identifies an elementary cate-gory, multiple elements of the same type can neither be differentiated nor properly computed in each domain/cycle of the derivation.
Thus, locality effects in language emerge from locality effects on brain activ-ity in relatively small populations of neurons, and ambiguactiv-ity in linguistic structure is the result of ambiguity in the sustainment of brain oscillations which are respon-sible for, among other things, identifying elements. Pursuing this kind of research in what has been named by Kopellet al.(2014) the ’dynomics’ framework, we are getting closer to reaching the implementational level of Marr (1982). In this sense, we might be able to explain why cognition has certain properties and not others from the physiological constraints of the circuits that generate it. This might be an adequate response to the kind of why question advocated in the minimalist pro-gram (Chomsky 1995): Why do we have the above-listed properties of cognition? Our answer is that we have them because we have those possible patterns of inter-actions in neural syntax, and not others.
2 Labeling Elements by Oscillatory Bands
I assume Boeckx’s (2014a) elementary categorization and develop his suggestion that elements are identified as a function of the concrete rhythm that forms and sustains their neural assemblies (Boeckx 2013). A first division can be done by claiming that non-PHs are sustained bygammaoscillations and PHs bybeta oscilla-tions. Furthermore, among PHs, twobetasub-bands may implement transitive and intransitive PHs:beta2andbeta1, respectively. As discussed below, intransitive PHs bear appealing resemblances to specifiers and internally merged elements, which prompts one to consider them as a single elementary category. The latter unifica-tion, in turn, will extend the explanatory reach considerably, but at the expense of some empirical reach.
These three rhythms are those sustained canonically by the cortex (Roopun
et al.2006, 2008). With layer 4 acting as a frontier (Maieret al.2010),gammais mainly registered in supragranular layers,beta2in infragranular layers, andbeta1emerges from the interaction of both infragranular and supragranular layers in certain cir-cumstances as described below. Furthermore, the layered dynamics distinction is reinforced by anatomic connections and the direction of the flow of information from these areas: Supragranular layers connect primarily with higher areas in a feedforward manner, whereas infragranular layers send feedback to the first and connect with subcortical structures such as the thalamus (Douglas & Martin 2004, Bastoset al.2012, Miller & Buschman 2013). Finally, different bands are discretized by different precise scales: A logarithmic scale around 2.16 that differentiates bands (Buzs´aki 2006) allows us to potentially differentiate two categories in thelow beta-gamma range, which would correspond to PHs and non-PHs, whereas a further discretizing golden mean of around 1.6 (Roopunet al.2008) offers us a new catego-rial distinction within thebetarange: transitive PHs for high and intransitive PHs for low beta. In short, the cortex offers anatomical, dynamic, information-dealing and ”mathematical” reflections of that ternary categorial distinction.
2.1 Unifying Intransitive PHs, Specifiers, and IMed elements
Before moving to specific labeling using oscillations, the extension of the categorial rhythmbeta1of intransitive PHs to specifiers and internally merged elements must be justified to some degree. First,an attempt will be done to unify specifiers and in-ternally merged elements. Afterwards, they will be unified with intransitive PHs.
From a more cognitive point of view, one interpretation of Uriagereka’s (1999) multiple Spell-Out model is that specifiers are always derived in parallel to the clausal spine. Although their fusion to the spine, cannot be strictly considered a case of IM, because the structure generated as a specifier is not contained in the spine, I argue that such a combination bears significant resemblances to the (sub)processes of IM. In this respect, IM has been theorized as being decomposed in copy and remerging (Corver & Nunes 2007).4 If we envisage the copy
nism as a more substantial availability in memory, with certain independence from its derivational history, this may be a feature required both by specifiers and inter-nally merged elements. Being derived in parallel as a specifier may require that elements be available longer than usual before being coupled to the clausal spine; this is also the case for internally merged elements which are susceptible to merg-ing operations longer. Independence from the derivational history may be reflected by the opacity of specifiers and moved elements for sub-extraction.
That copy-like mechanism, consisting of a longer holding in working mem-ory, is a defining feature of the genesis and sustainment of beta1oscillations (see below). Thus, at least to a certain point, we can abstract significant commonalities between specifiers and internally merged elements, converging on the attributes of thebeta1rhythm. This hypothesis makes further sense if we consider the position where internally merged elements land: It is always a specifier-like position, which is also the case for the edge in phases.
The next step to confer plausibility to the intended unification is to find signif-icant commonalities between specifiers/internally merged elements and intransi-tive phases. In this respect, Boeckx (2014a) argues that specifiers are always intran-sitive phases, which is what prevents external systems suffering an anti-identity violation, where the combination of the PH of the current derivational stage and the PH merged to its edge takes place. As a matter of fact, in Boeckx’s (2014a) the-ory, there is only one intransitive PH in each derivation apart from the specifiers, which is the one precisely at the bottom of the structure (consider how problematic that derivational point has always been in terms of labeling, etc.).
This not only equates intransitive PH and specifiers to a certain degree (and, by extension, internally merged elements), but also discards the other structures (adjuncts) derived in parallel that could be related tobeta1as well. Boeckx (2014a) argues that adjuncts are transitive PHs that lead to anti-identity violations in their merge and from which islands, due to a forced transfer, could arise. Furthermore, the aforementioned fact that intransitive heads are those that initiate the deriva-tion significantly connects with how that beta1rhythm is evoked: to be exact, by novel/unfamiliar elements, which can be interpreted as the beginning of each (par-allel) derivation.
2.2 Rhythmic Gamma, Beta2, and Beta1 Labels
The purpose of this section is to justify why these specific rhythms are assigned to their concrete categories. Regarding non-PHs, the essential idea is that they are objects with less combinatorial potential or are simpler. I attributegammato non-PHs by considering the formation of neural words from Buzs´aki’s (2010) theory of neural syntax and the role gamma plays in binding features into coherent ob-jects, which could be concepts lexicalized later (Buzs´aki 2006, Bosman et al.2014, Honkanenet al.2014).
The observation that there is an increase ofgammaactivity as more items are represented or held (Roux & Uhlhaas 2014) suggests thatgammarepresents the con-tents of working memory (Honkanenet al.2014) as well as items in language (see discussion below on the disambiguation of gamma and betaroles). Furthermore,
conduc-tion delays (von Stein & Sarnthein 2000, Buzs´aki 2006), all of which connects to their simplified nature with respect tobetaPHs.5
The main property of PHs is that, due to a longer syntactic life, they are more complex than non-PHs in the sense that they act as linkers between themselves and among derivational stages. Such a complexity difference betweengammaandbeta
has already been shown by Honkanenet al.(2014) in the representation of objects in visual working memory, with the more complex being represented by beta as opposed to gamma. Furthermore, in implementational terms, further complexity may also require the recruitment of a larger neural population, which is in line with the slowing down ofgammarhythms until they reachbetaonce PHs are labeled.
I attributebetato PHs by taking into account the functional role of sustaining thestatus quo attributed to the rhythm in working memory (Engel & Fries 2010). Although there is ambiguity in the literature aboutgammaandbetain the function of holding items (Dipoppa & Gutkin 2013), there is accumulating evidence to ul-timately disambiguate it, and to claim that onlybetais the rhythm responsible for holding objects (Tallon-Baudry et al.2004, Deiber et al.2007, Engel & Fries 2010, Parnaudeau et al.2013, Salazar et al. 2012, Martin & Ravel 2014), whereasgamma
forms them initially. What defines PHs is that they have a longer merging life, which particularly enables them to be related to more elements. This is visible in the construction of the clausal spine over PHs embedding complements, where PHs function as links between different derivational phases and local domains—they re-main at the edge, which enables them to be in at least two phases. Thus, it makes sense that PHs must be cognitive sets held longer in working memory by means ofbeta, which might be the capacity that allows us to transcend the computational complexity of finite state machines (Chomsky 1957).
In addition, the phase-edge presents a computational requirement that has also been noted in goal-directed behavior. One of the functions of PHs remaining at the edge when transfer takes place is to integrate the results of different deriva-tional stages, as heads in phrases integrate complements and specifiers, which, as defended, might be the same case. Equally, Duncan (2013) argues that complex tasks are divided into hierarchically organized sub-goals, which he considers at-tentional episodes and which must be executed in the proper sequence to accom-plish the final objective. Thus, both in the phase-edge and in the succession of attentional episodes, the results of one sub-process must be communicated to the next. Crucially, it is assumed that these kinds of processes require top-down con-trol, which is a mechanism usually attributed tobetabands (Bastoset al.2015).
The latter argument in favor ofbeta-holding PHs has to do with basal gan-glia implications. Namely, thatbetaholding in memory mechanism can be under-stood as a selection mechanism provided by the basal ganglia, typically explained as one of its loops being disinhibited, thus favoring one (motor) representation at the expense of others (Koziol et al. 2009). Cannon et al. (2014) and Antzoulatos & Miller (2014) point to basal ganglia precisely as a corticalbetagenerator which, when added to evolutionary considerations (Buzs´akiet al.2013), suggests
embrac-5 The consistencies with cognitive neuroscience are stronger in Ram´ırezet al.’s (2015) model. Following Boeckx’s (2014a) labeling by phase theory, it is argued that all items are born as
ing Maieret al.’s (2010) hypothesis that subcortical rhythmogenesis of slow rhythms are detected in infragranular cortical layers. Thus, a coherent picture emerges with respect to PHs where basal ganglia, infragranular cortex,beta, and holding elements converge on a single mechanism.
Now, a further distinction among PHs can be made: beta2for transitive PHs andbeta1for intransitive PHs (specifiers/internally merged elements). This could also help to disambiguate, in Cannonet al.’s (2014: 714) terms, the ”mystery of mul-tiplebetarhythms”. The strongest arguments I can provide are threefold: (i) related to the fact that intransitive PHs are the beginning of each derivation and beta1is caused by unfamiliar or novel elements, (ii) related to what has been described as one sub-process of movement,beta1genesis occurs from previousbeta2andgamma, in a copy-like fashion, and (iii) related to the longer syntactic availability of intran-sitive PHs, moved elements and specifiers, beta1 presents the capacity to sustain representations in absence of inputs. Now, each of these points will be developed.
First, Kopellet al.(2010) note thatbeta1rhythm is unchained by unfamiliar, as opposed to familiar, elements. The first can be reinterpreted as novel elements and extended to those initiating a new process. Similarly, Boeckx (2014a) argues that intransitive PHs are those that always initiate the derivation. This strikes me as highly similar, that is to say, the novelty of both PHs and unfamiliar elements. Considering the discussion above, if phase heads are sustained by beta, it makes sense to think that the more novel process has to do with the initiation of the deriva-tion and, therefore, unchainsbeta1.6
Second, with regard to the copy sub-process of movement,beta1genesis may shed light on the issue. Beta1 rhythm emerges when a period of high excitation decays, andgammain supragranular layers andbeta2in infragranular layers begin to interact and reset each other (Krameret al.2008). The result of that interaction, which implies a transient ’fusion’ of supragranular and infragranular layers, is that their phases are added up: ”[T]he period [ofbeta1] (65 ms) is the sum of the natural periods (25 ms [ofgamma] and 40 ms [ofbeta2]) of the excitable oscillators” (Kramer
et al. 2008: 2) (see also Roopunet al.2008). For thatbeta1rhythm to arise, then, the ”initial interval of coexistent gamma and beta2” preceding the new oscillation is crucial (Krameret al.2008: 2).
If labeling PHs is obtained by slowing down the rhythm that initially sus-tained the assembly of the item from gamma to beta, whatbeta1 genesis suggests would be a second labeling after the first one, a sort of dual process. In the first step, the initial part of the process would be when the assembly that represents the exter-nally merged PH oscillates atbeta2in the period of high excitation, and the supra-granular layers atgammareceive a kind of feedback or top-down signal asbeta2in the infragranular cortex. Later, when excitation decays, a second labeling-like op-eration would take place. Thus, the second part of the process would be a slowing down of the assembly and the fusing of the infragranular and supragranular layers into a singlebeta1rhythm. That latter sub-process as a sort of copy/second labeling is strikingly similar to the decomposition of movement operation in early minimal-ism (Chomsky 1993): Merge and label initially the PH usingbeta2and then copy it usingbeta1.
As discussed above, intransitive PHs, moved elements, and specifiers are closely related: If specifiers are derived in parallel, then maybe what is actually embedded in the clausal spine is really a copy of their PH which, as discussed, is certainly the case for intransitives. This copy-like mechanism not only resembles explanations given in linguistics at a computational level; it also leads to another property that crucially defines internally merged elements: their longer availability to syntax, which leads us to the next argument.
Third, when considering the idea that the internally merged element must be available longer,beta1again provides an appealing parallelism. In this respect, Kopell et al. (2010, 2011) provide crucial insights by looking at the physiological properties of the rhythm. They note thatbeta1dependence on inhibitory rebound allows it ”to continue in the absence of continuing input” (Kopell et al. 2010: 3), providing memory for the objects. That extra memory might be just what enables internally merged intransitive PHs to be available longer to syntax. Furthermore, Kopellet al. (2011) note that withinbeta1, different assemblies (at gamma) can co-exist without so much competition between them, which creates a context for si-multaneously coding the past and present and relating temporally segregated ob-jects. It is hard for a linguist not to read these different past and current elements as being the different relationships that the occurrences or copies of moved elements establish. So,beta1is perfect for comparing new and old information and putting together information from different modalities because of its wider temporal win-dows rather than faster rhythms (see Senkowskiet al.2008 and in particular Dean
et al. 2012). The same hypothesis of an extended window of integration without further input and without much competition between elements is consistent with sustaining thestatus quoas suggested by Engel & Fries (2010) discussed above.
Furthermore, there are two additional considerations that may reinforce la-beling bybeta1: That rhythm stops when the excitation decays too much, or when it is reactivated and replaced bybeta2andgamma (Cannonet al.2014). From both versions of finishing the rhythm, two properties of movement could be inferred. When it decays too much, movement could be barred because of memory limita-tions. When the cortex is reactivated and beta1is replaced bybeta2, the twobeta2
rhythms could be related to the maximum of two interpretative positions in chains (Boeckx 2012), which is usually attributed to a complete valuation of unvalued features (Chomsky 2000, 2001), barring third interpretative positions for internally moved elements.
Last but not least, when there isbeta1in the cortex, there is less competition among assemblies (Kopell et al. 2011). This could be correlated to why PHs (at
beta2) can be connected to both complements (atgamma) and specifiers (at beta1), despite the strong prohibition against *XX oscillations and categories, and to why adjuncts, which might be assemblies oscillating atbeta2, show stronger constraints on movement or are more opaque.
PHs as more familiar/less newer elements (Kopell et al.2011); therefore, they do not causebeta1. Furthermore, if the remainder of the discussion is also on the right track, there is no space for assigning transitive PHs in the oscillatory spectral range I circumscribed the operations to. The ideal scenario would be a strong disam-biguation of the functional roles ofbeta1andbeta2rhythms, but in this respect the literature has yet to make this point clear. Thus, although we should expect fur-ther theoretical refinement, fur-there is no significant counterargument for considering
beta2as being the rhythm responsible for transitive PHs.
3 Ambiguous Synchrony and Short (and Apparently Long) Anti-locality
In the previous section, a way to categorially distinguish three elements as a func-tion of the rhythms that sustain them has been developed. Non-PHs would oscillate atgamma, transitive PHs atbeta2and intransitive PHs atbeta1. As summarized in Section 1, in certain domains external systems cannot interpret *XX-like construc-tions. This, translated in oscillatory terms, means that certain brain structures are unable to sustain more than one of those rhythms in each band. So, the constraint can be formulated in the following way: What kind of system cannot sustain mul-tiple rhythms in the same band?
I hypothesize that this is the case of a system that is too local or too small. The brain tends to synchronize its activity in the form of coupled oscillations (Buzs´aki 2006). That coupling depends, among other factors, on the distance that separates the neurons. In other words, if the distance is long then there are only certain rhythms that are slow and powerful enough to synchronize cells. In contrast, when the structure is local/small, even fast rhythms are able to acquire the population in-phase. The latter is potentially the case for the language-specific sub-regions in external systems. Within these sub-regions, neurons are so close that their natural tendency towards synchrony forces them to be coupled even in fast rhythms. Thus, if there is a rhythm in thebeta-gammaband, it will recruit the whole population at the specific oscillatory band regardless of whether independent neurons begin to oscillate independently. In fact, they will be synchronized far too early for multiple assemblies to be differentiated within the same band. Since labeling depends on how many of these rhythms can be sustained, only one category can be identified in each band.
This enables us to explain the linguistic manifestation of those rhythmic lim-ited patterns, and the structural constraints of phrases and phases. It has been argued that phrases contain a maximum of one head, one complement, and one specifier (see Boeckx 2008 for a feature-valuation approach and Kayne 1994 for one in terms of linearization). My proposal about labeling and anti-identity can explain that ternary structure, as (6) makes evident. There, a maximum of three distinct ele-ments can co-exist in a local domain: onegamma/complement item, onebeta2/head item, and onebeta1/specifier item.7
(6) a. [... head [ complement specifier head [...]] ] b. [...beta2[gamma beta1 beta2[...]] ]
Thanks to the unification of phrases and phases, this ternary structure above can be extended to phase-structure (7). Furthermore, the distinction between tran-sitive and intrantran-sitive PHs into sub-bands ofbetaenables us to explain why two-phase heads can co-exist without violating the anti-identity constraint.
(7) a. [... C [ T (EA)v[...]]]
b. [... transitive-PH [ non-PH (intransitive-PH/edge) transitive-PH [...]] ] c. [...beta2[gamma(beta1)beta2[...]] ]
Following the logic of the present model, if we assume that there is only a maximum of one non-PH and one transitive-PH in transferred phase complements (Boeckx 2014a) (with optional specifiers as intransitive-PH embedded in the latter), it is also possible to explain the rhythmic nature of the derivation of the clausal spine, with PHs and non-PHs alternating (Richards 2010) (8). The fact is that more than onegammacannot be sustained and more than onebeta2cannot either at cer-tain derivational stages, which forces the clausal spine to be formed in that rhyth-mic fashion.
(8) a. ...[C [Tv[Vn[N] ] ] ]
b. ...[PH [non-PH PH [non-PH PH [non-PH] ] ] ] c. ...[beta[gamma beta[gamma beta[gamma] ] ] ]
Once we differentiate further between the types of PHs (transitive and in-transitive), the pattern above, which is limited to a maximum of one element of a particular category in a phase complement, can explain more typical anti-identity violations. In (9a), twobeta1/intransitive-PHs cannot coexist in that local domain. On the contrary, as (9d) shows, when we extract one of these conflicting oscillations, the rhythmic patterns become sustainable, since one of thebeta1sthen co-exists with onebeta2in the next domain/derivational cycle.
(9) a. *sono
are
[queste
these
foto
pictures
del
of-the
muro]
wall
[la
the
causa
cause
della
of-the
rivolta]. Italian riot
’These pictures of the wall are the cause of the riot’
(Moro 2000)
b. *transitive-PH [non-PH(V, be) intransitive-PH intransitive-PH] c. *beta2[(gamma)beta1 beta1]
d. [Queste these foto pictures del of-the muro wall sono are [la the causa cause della of-the rivolta]]. Italian riot
’These pictures of the wall are the cause of the riot’
e. *[intransitive-PH transitive-PH [gamma(V, ser) intransitive-PH]] f. *[beta1 beta2 [(gamma)beta1] ]
The same logic can be extended to the ambiguous ungrammatical co-existence of two transitive PHs, which prohibits constructions like (10a). However, turning one of these transitive PHs into one intransitive PH solves the impossible sustain-ment of twobeta2rhythms (10d). Furthermore, (10a) impossible sustainment of two
beta2rhythms in locality might represent the case of adjuncts and islands, generally speaking, if we follow Boeckx’s (2014a) idea that adjuncts, in contrast to specifiers, are often structurally equivalent to the transitive-PH they adjoin to. The latter could then explain the less opaque nature of specifiers to sub-extraction, for example, sincebeta1andbeta2co-existence is possible; this is not the case with two beta2in adjunction.
(10) a. *Describieron
described [a to un a maestro master de of Zen] zen [al to-the papa]. pope Spanish
’They described a Zen master to the pope’.
(Richards 2010) b. *transitive-PH [non-PH transitive-PH transitive-PH]
c. *beta2[gamma(V,describir)beta2 beta2] d. Describieron described [un a maestro master de of Zen] zen [al to-the papa]. Spanish pope
’They described a Zen master to the pope’.
e. transitive-PH [non-PH intransitive-PH transitive-PH ] f. beta2[gamma(V,describir)beta1 beta2]
Given the potential equivalence between anti-identity and anti-locality dis-cussed in Section 1, the same explanation given for (9)—(10) can account for *XX conflicts in structures like (11). If such an hypothesis is on the right track, it could offer ”the kind of ’deeper’ explanation on independent grounds” that Grohmann (2011: 271) pursues.8
8 However, the repair strategy of spelling out the lower occurrence of the conflicting element is not transparent.
... [Johnilikes himselfi]. (adapted from Grohmann 2011)
... [intransitive-PH non-PH ??] ... [beta1 gamma?? ]
(11) a. *... [Johnilikes ti].
(adapted from Grohmann 2011) b. * ... [intransitive-PH non-PH intransitive-PH]
c. * ... [beta1 gamma beta1]
Finally, if we continue to assume that internally merged elements are held by beta1, we can also explain the *XX intervention effect of movement discussed in Section 1. Chomsky (2013) notes that labeling problems with XP—XP structures can be extended to constraints on movement over intervening elements. All we have to do is reduce locality across domains to locality within domains, represented by the cyclic nature of IM. As (12) makes clear, when onebeta1internally merged element coexists in a derivational stage with another one, *XX constraints arise in the form of twobeta1. As detailed earlier, both oscillations are impossible to sustain, because we are again trying to sustain two rhythms in the same (beta1) band, and a minimality effect arises.
(12) a. *How do you wonder [ who (how)v[behaved (how)] ]?
(Rizzi 2011) b. * PH [... intransitive-PH intransitive-PH transitive-PH [non-PH...] ]
c. *beta2[...beta1 beta1 beta2[gamma..] ]
Despite its empirical and explanatory reach, my model faces a problem: There is no anti-identity violation when, due to cyclic IM, one moved element co-exists with one specifier (13).
(13) a. How do you think ... [ he (how)v[behaved (how)] ]?
b. PH [... intransitive-PH (intransitive-PH) transitive-PH [non-PH ...]] c. beta2[...beta1 beta1 beta2[gamma..] ]
However, the problem my proposal faces here is not exclusive to it. One of the lessons in generative linguistics is that the more linguistic data are anayzed in detail, the more exceptions to explanatory theories there are. The phenomena of adjuncts, specifiers, islands, and so on are not fully satisfied nor in Kayne (1994) nor in Uriagereka (1999). Nevertheless, it does not prevent these theories from be-ing some of the most elegant and inspirational ones to have led investigations in the field. Relatively speaking, we should not simply discard the present model because of some counterarguments from data coming from isolated linguistic de-bates (but see Leivada 2015 for discussion from a biolinguistic approach, and see Section 5 about experimental data). In this respect, inspiration may come from cognitive neuroscience: Conflicting evidence about the functional role ofalpha os-cillations did not discourage pursuing good intuitions; on the contrary, they have led to fruitful debates and a much deeper understanding of rhythm (see Palva & Palva 2007, 2011, and references therein).
It may be better to leave conflicting data to further inquiry, since it has been shown that the ambiguous synchronization of oscillations in local brain structures can potentially account for the ternary structure of phrases (6) and phases (7), the rhythmic nature of clausal linguistic structures (8), anti-identity constraints (9)— (10) extendable to adjuncts in the case of transitive PHs, anti-locality (11), and in-tervention effects in IM (12). Crucially, just a single common principle can explain the main linguistic properties: The brain synchronizes its activity (locally). The de-gree of plausibility in that kind of explanation allows it worth pursuing, even if this paper turns out to be completely wrong in its implementation.
4 From Global to Local: Periphery Constraining the Core
The present model also represents, in a seductive way, a lax interpretation of the distinction between I-language and E-language (Chomsky 1986). I-language should be understood here as a global, domain-general computational system, while E-language would be a more local and specific system or an interface which the for-mer connects to. Before transfer to external systems, a domain-general large-scale core set of regions would be used. Thus, we work on a global scale that governs the freer syntax of I-language. However, after transfer, when rhythms are circum-scribed to the cortical limitations of external systems, we move to local structures and to sub-regions of the Broca—Wernicke network. We are, in fact, moving from global to local in that transition to what can be represented in E-language. That E-language domain would impose constraints which cannot be expected in the net-work of I-language because the latter has more computational power thanks to the subcortical sources of slower rhythms.
of a higher complexity.
This kind of constraint at certain local and peripheral structures of a system can be exploited by other theories which deal with locality conditions and capac-ity limits. As mentioned earlier, these kinds of cognitive limitations have been ap-proached from different perspectives, for instance: (1) regarding the limits of global workspace for consciousness, Min (2010) argues that the limited capacity of atten-tion and consciousness is due to the mechanical limitaatten-tions of the thalamic reticu-lar nucleus synchronizing processes;9 (2) regarding attention, Miller & Buschman (2013) speak broadly about a limited ’bandwidth’; (3) regarding working mem-ory limits, Lisman (2010) argues for a maximum of 7±2gammacycles representing items embedded in a singletheta cycle, which is exportable to the limitation to 4 items in the interaction of gamma andalpha (Roux & Uhlhaas 2014); or (4), alter-natively, Palvaet al.(2010) attribute visual working memory limits to a bottleneck effect of oscillations in a hub like the intraparietal sulcus.
Nevertheless, there is, as far as I know, no explanation like the one offered here, where the constraint does not come from the core of the system itself but rather from the periphery to which it connects. This, furthermore, is reinforced by a solid theoretical background in generative grammar that, in this respect, has not changed in recent times. The distinction between I-language and E-language has al-ready been related to the observation that external systems impose constraints that would not otherwise be expected, such as pronouncing only one copy of internally merged elements. In sum, a complementary explanation of capacity limitations may come from peripheral structures.
5 Conclusions: The Unexplored Dimension of Broca’s Problem
Joining Kopellet al.’s (2014) framework of ’dynomics’, it seems possible to explain why cognition has certain properties and not others from the physiological con-straints of its brain circuits, understood as dynamic structures with activity at a real time scale rather than as more or less static maps that are mainstream in neu-rolinguistics (Poeppel 2012).
This approach has drawn our attention to the temporal dimension on multi-ple scales of brain activity (Buzs´aki 2010), which allows a mechanistic explanation of what bars certain syntactic derivations and, consequently, what defines some crucial properties of linguistic structures.
That sort of answer suits the minimalistwhyquestion, namely why language has certain properties and not others (Chomsky 1995). It does so from an inter-disciplinary perspective, fusing neuroscience and linguistics. Such a methodol-ogy not only offers a more solid, deeper, and less falsifiable answer, but also pro-vides bridges to other levels of research, from genome to phenome (Boeckx & Theofanopoulou 2014), since, as Siegelet al.(2012) suggest, brain rhythms lie just in the middle across various levels of research.
Thus, this article not only contributes to biolinguistics in the strong sense
(Boeckx & Grohmann 2007a) along the lines of Giraud & Poeppel (2012) in the realm of phonology, but also confers theoretical plausibility and pursues Boeckx
& Benítez-Burraco’s (2014) invitation to explore a new dimension of Broca’s prob- lem: Brain oscillations.
It seems possible to explain that some principles can be reduced to a physical and general restriction over brain/language/mind structure: Peripheral (language) systems are far too local to sustain multiple rhythms in the same band by which elements are identified.
Of course, the present work is mainly theoretical, so hopefully some empir- ical testing will, in the future, shed more light on the issues at hand. As a first and specific example, electroencephalographies should not register more than
one gamma, one beta1 and one beta2 oscillation in cortical sub-regions of the
Broca—Wernicke network. If they were registered, they should be coupled as single oscillations in very few cycles. Alternatively, due to the interdisciplinary approach of my model, a similar locality effect could be registered in regions usually associated with other cognitive domains and even involving other (fast) rhythms. Then, support may come from neuroscience studies beyond the field of linguistics. Time will tell.
References
Antzoulatos, Evan G. & Earl K. Miller. 2014. Increases in functional connectivity between prefrontal cortex and striatum during category learning. Neuron 83 (1), 216–225.
Bastos, Andre M., W. Martin Usrey, Rick A. Adams, George R. Mangun, Pascal Fries, & Karl J. Friston. 2012. Canonical microcircuits for predictive coding.
Neuron 76(4), 695–711.
Bastos, Andre M., Julien Vezoli, & Pascal Fries. 2015. Communication through coherence with inter-areal delays. Current Opinion in Neurobiology 31, 173– 180.
Boeckx, Cedric. 2003. Islands and Chains: Resumption as Stranding. Amsterdam: John Benjamins.
Boeckx, Cedric. 2007. Some notes on bounding. Language Research 43, 35–52. Boeckx, Cedric. 2008. Bare Syntax. Oxford: Oxford University Press.
Boeckx, Cedric. 2010. Defeating lexicocentrism: Part a of elementary syntactic structures. Ms., ICREA/UAB.
Boeckx, Cedric. 2012. Syntactic Islands. Cambridge: Cambridge University Press. Boeckx, Cedric. 2013. Merge: Biolinguistic considerations. English Linguistics 30
(2), 463–484.
Boeckx, Cedric. 2014a. Elementary Syntactic Structures: Prospects of a Feature-Free
Syntax, volume 144. Cambridge: Cambridge University Press.
Boeckx, Cedric, 2014b. The role of the thalamus in linguistic cognition. Ms.,
ICREA/UB.
Boeckx, Cedric & Antonio Benítez-Burraco. 2014. The shape of the human language-ready brain. Frontiers in psychology 5.
Boeckx, Cedric & Kleanthes K. Grohmann. 2007b. Remark: Putting phases in perspective. Syntax 10(2), 204–222.
Boeckx, Cedric & Constantina Theofanopoulou. 2014. A multidimensional inter- disciplinary framework for linguistics: The lexicon as a case study. Journal of
Cognitive Science 15, 403–420.
Bosman, Conrado A., Carien S. Lansink, & Cyriel Pennartz. 2014. Functions of gamma-band synchronization in cognition: From single circuits to functional diversity across cortical and subcortical systems. European Journal
of Neuroscience.
Buzsáki, György. 2006. Rhythms of the Brain. Oxford: Oxford University Press. Buzsáki, György. 2010. Neural syntax: Cell assemblies, synapsembles, and
readers. Neuron 68(3), 362–385.
Buzsáki, György & Andreas Draguhn. 2004. Neuronal oscillations in cortical net- works. Science 304(5679), 1926–1929.
Buzsáki, György & Brendon O. Watson. 2012. Brain rhythms and neural syntax: Implications for efficient coding of cognitive content and neuropsychiatric disease. Dialogues in Clinical Neuroscience 14(4), 345.
Buzsáki, György, Nikos Logothetis, & Wolf Singer. 2013. Scaling brain size, keeping timing: Evolutionary preservation of brain rhythms. Neuron 80(3), 751–764.
Cannon, Jonathan, Michelle M. McCarthy, Shane Lee, Jung Lee, Christoph Börgers, Miles A. Whittington, & Nancy Kopell. 2014. Neurosystems: Brain rhythms and cognitive processing. European Journal of Neuroscience 39(5), 705–719.
Chomsky, Noam. 1957. Syntactic Structures. Berlin: Mouton de Gruyter.
Chomsky, Noam. 1986. Knowledge of Language: Its Nature, Origin, and Use. Westport: Greenwood Publishing Group.
Chomsky, Noam. 1993. A minimalist program for linguistic theory. The minimalist
program, 167–217.
Chomsky, Noam. 1995. The Minimalist Program, volume 28. Cambridge: Cambridge University Press.
Chomsky, Noam. 2000. Minimalist Inquiries: The framework. In Step by step: Essays
on minimalist syntax in honor of Howard Lasnik, ed. by Roger Martin, David
Michaels, and Juan Uriagereka, 89–155. Cambridge, MA: MIT Press.
Chomsky, Noam. 2001. Derivation by phase. In Ken Hale: A life in Language, ed. by Michael Kenstowicz, 1-52. Cambridge, MA: MIT Press.
Chomsky, Noam. 2013. Problems of projection. Lingua 130, 33–49.
Corver, Norbert & Jairo Nunes. 2007. The Copy Theory of Movement. Amsterdam: John Benjamins.
Dean, Heather L., Maureen A. Hagan, & Bijan Pesaran. 2012. Only coherent spiking in posterior parietal cortex coordinates looking and reaching.
Neuron 73(4), 829–841.
Dipoppa, Mario & Boris S. Gutkin. 2013. Flexible frequency control of cortical oscillations enables computations required for working memory.
Proceedings of the National Academy of Sciences 110(31), 12828–12833.
Douglas, Rodney J. & Kevan A.C. Martin. 2004. Neuronal circuits of the neocortex. Annual Review of Neuroscience. 27, 419–451.
Duncan, John. 2013. The structure of cognition: Attentional episodes in mind and brain. Neuron 80(1), 35–50.
Engel, Andreas K. & Pascal Fries. 2010. Beta-band oscillations — signalling the status quo? Current Opinion in Neurobiology 20(2), 156–165.
Engel, Andreas K. & Wolf Singer. 2001. Temporal binding and the neural correlates of sensory awareness. Trends in Cognitive Sciences 5(1), 16–25. Epstein, Samuel David & T. Daniel Seely. 2002. Rule applications as cycles in a
level-free syntax. Derivation and Explanation in the Minimalist Program, 65–89. Fedorenko, Evelina & Sharon L. Thompson-Schill. 2014. Reworking the language
network. Trends in Cognitive Sciences 18(3), 120–126.
Friederici, Angela D. 2011. The brain basis of language processing: From structure to function. Physiological Reviews 91(4), 1357–1392.
Fries, Pascal. 2005. A mechanism for cognitive dynamics: Neuronal communi-cation through neuronal coherence. Trends in Cognitive Sciences 9(10), 474– 480.
Giraud, Anne-Lise & David Poeppel. 2012. Cortical oscillations and speech processing: Emerging computational principles and operations. Nature
Neuroscience 15(4), 511–517.
Gray, Charles M. & Wolf Singer. 1989. Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proceedings of the National Academy
of Sciences 86(5), 1698–1702.
Grohmann, Kleanthes. 2000. Prolific Peripheries: A Radical View from the Left. PhD thesis.
Grohmann, Kleanthes. 2011. Anti-locality: Too-close relations in grammar. In The
Oxford Handbook of Linguistic Minimalism. Oxford: Oxford University Press.
Hale, Kenneth & Samuel Jay Keyser. 1993. On argument structure and the lexical expression of syntactic relations. The View from Building 20, 53-109.
Hebb, Donald. 1949. The Organization of Behavior.
Heck, Fabian & Gereon Müller. 2000. Successive cyclicity, long-distance superiority, and local optimization. In Proceedings of WCCFL 19, 218–231. Honkanen, Roosa, Santeri Rouhinen, Sheng H. Wang, J. Matias Palva, & Satu
Palva. 2014. Gamma oscillations underlie the maintenance of feature-specific information and the contents of visual working memory. Cerebral Cortex.
Katz, Jerrold J. 1964. Current issues in linguistic theory. In The Structure of
Language: Readings in the Philosophy of Language. Prentice Hall.
Kayne, Richard S. 1994. The Antisymmetry of Syntax. MIT Press.
Kopell, N., M.A. Whittington, & M.A. Kramer. 2011. Neuronal assembly dynamics in the beta1 frequency range permits short-term memory.
Proceedings of the National Academy of Sciences,108(9), 3779–3784.
Neuroscience 4.
Kopell, Nancy J., Howard J. Gritton, Miles A. Whittington, & Mark A. Kramer. 2014. Beyond the connectome: The dynome. Neuron 83(6), 1319–1328.
Koziol, Leonard F., Deborah Ely Budding, & Andrew Suth. 2009. Subcortical
Structures and Cognition. Springer.
Kramer, Mark A., Anita K. Roopun, Lucy M. Carracedo, Roger D. Traub, Miles A. Whittington, & Nancy J. Kopell. 2008. Rhythm generation through period concatenation in rat somatosensory cortex. PLoS Computational Biology 4(9).
Lahne, Dikken. 2012. The locality of syntactic dependencies. In The Cambridge
Handbook of Generative Syntax. Cambridge, UK: Cambridge, UK, 655-697..
Larson, Richard K. 1988. On the double object construction. Linguistic Inquiry, 335–391.
Leivada, Evelina. 2015. X-within-X structures and the nature of categories.
Biolinguistics 9.
Lisman, John. 2010. Working memory: The importance of theta and gamma oscilla- tions. Current Biology 20(11), 490–492.
Maier, Alexander, Geoffrey K. Adams, Christopher J. Aura, & David A. Leopold. 2010. Distinct superficial and deep laminar domains of activity in the visual cortex during rest and stimulation. Frontiers in Systems Neuroscience, 4–31. Marr, David. 1982. Vision: A computational investigation into the human repre-
sentation and processing of visual information.
Martin, Claire & Nadine Ravel. 2014. Beta and gamma oscillatory activities associated with olfactory memory tasks: Different rhythms for different functional networks? Frontiers in Behavioral Neuroscience 8, 218.
Miller, Earl K. & Timothy J. Buschman. 2013. Cortical circuits for the control of attention. Current opinion in neurobiology 23(2), 216–222.
Min, Byoung-Kyong. 2010. A thalamic reticular networking model of consciousness. Theoretical Biology and Medical Modeling 7(10).
Moro, Andrea. 2000. Dynamic Antisymmetry. Cambridge: MIT Press.
Müller, Gereon. 2004. Phrase impenetrability and wh-intervention. In Minimality
Effects in Syntax, 289–325.
Müller, Gereon. 2011. Constraints on Displacement: A Phase-Based Approach. Amsterdam: John Benjamins Publishing.
Narita, Hiroki. 2012. Phase cycles in service of projection-free syntax. In Phases:
Developing the framework. Berlin: Mouton de Gruyter.
Palva, J. Matias, Simo Monto, Shrikanth Kulashekhar, & Satu Palva. 2010. Neuronal synchrony reveals working memory networks and predicts individual memory capacity. Proceedings of the National Academy of Sciences
107(16), 7580–7585.
Palva, Satu & J. Matias Palva. 2007. New vistas for α-frequency band oscillations.
Trends in neurosciences 30(4), 150–158.
Palva, Satu & J. Matias Palva. 2011. Functional roles of alpha-band phase synchro- nization in local and large-scale cortical networks. Frontiers in Psychology 2.
Kellendonk. 2013. Inhibition of mediodorsal thalamus disrupts thalamofrontal connectivity and cognition. Neuron 77(6), 1151–1162.
Poeppel, David. 2012. The maps problem and the mapping problem: Two challenges for a cognitive neuroscience of speech and language. Cognitive
neuropsychology 29(1-2), 34–55.
Ramírez, Javier. 2014. Sintaxis oscilante. MA Thesis.
Ramírez, Javier, Constantina Theofanopoulou, & Cedric Boeckx. 2015. A hypothesis concerning the neurobiological basis of phrase structure building. Ms. UB/UdG.
Richards, Norvin. 2010. Uttering Trees. Cambridge, Mass.: MIT Press. Rizzi, Luigi. 1990. Relativized Minimality. Cambridge, Mass.: MIT Press.
Rizzi, Luigi. 2011. Minimality. In The Oxford Handbook of Linguistic Minimalism, 220–238. Oxford: Oxford University Press.
Roopun, Anita K., Steven J. Middleton, Mark O. Cunningham, Fiona E.N. LeBeau, Andrea Bibbig, Miles A. Whittington, & Roger D. Traub. 2006. A beta2-frequency (20–30 hz) oscillation in nonsynaptic networks of somatosensory cortex. Proceedings of the National Academy of Sciences 103(42), 15646–15650.
Roopun, Anita K., Mark A. Kramer, Lucy M. Carracedo, Marcus Kaiser, Ceri H. Davies, Roger D. Traub, Nancy J. Kopell, & Miles A. Whittington. 2008. Period concatenation underlies interactions between gamma and beta rhythms in neocortex. Frontiers in Cellular Neuroscience 2.
Roux, Frédéric & Peter J. Uhlhaas. 2014. Working memory and neural oscilla- tions: Alpha–gamma versus theta–gamma codes for distinct wm information? Trends in Cognitive Sciences 18(1), 16–25.
Salazar, Rodrigo F., Nicholas M. Dotson, Steven L. Bressler, & Charles M. Gray. 2012. Content-specific fronto-parietal synchronization during visual working memory. Science 338(6110), 1097–1100.
Senkowski, Daniel, Till R. Schneider, John J. Foxe, & Andreas K. Engel. 2008. Crossmodal binding through neural coherence: Implications for multisen- sory processing. Trends in Neurosciences 31(8), 401–409.
Siegel, Markus, Tobias H. Donner, & Andreas K. Engel. 2012. Spectral fingerprints of large-scale neuronal interactions. Nature Reviews
Neuroscience 13(2), 121–134.
Tallon-Baudry, Catherine, Sunita Mandon, Winrich A. Freiwald, & Andreas K. Kreiter. 2004. Oscillatory synchrony in the monkey temporal lobe correlates with performance in a visual short-term memory task. Cerebral Cortex 14(7), 713–720.
Uriagereka, Juan. 1999. Multiple spell-out. In Working Minimalism, edited by Samuel Epstein & Norbert Hornstein, 251-282. Cambridge, Ma.: MIT Press. Stein, Astrid von & Johannes Sarnthein. 2000. Different frequencies for different
Javier Ramírez Fernández Universitat de Girona
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